ZURICH (Reuters) - Iranian President Hassan Rouhani will visit neutral European neighbours Switzerland and Austria next month, the Swiss and Austrian governments said, on a trip overshadowed by the looming imposition of U.S. economic sanctions on Tehran.

President Donald Trump in May pulled the United States out of an international nuclear deal with Iran and said he would reimpose harsh sanctions on Tehran, upsetting European allies who have scrambled to preserve ties.

Switzerland, which is not a member of the European Union, represents the interests of the United States and Saudi Arabia in Iran and of Iran in Saudi Arabia. Mainly Shi’ite Muslim Iran and Sunni powerhouse Saudi Arabia are rivals in the Middle East.

Iranian television said officials and business executives would accompany Rouhani on the trip, during which several cultural, economic and political agreements would be signed.

The Swiss government said Rouhani and Foreign Minister Mohammad Javad Zarif would attend meetings on July 2 and 3 with four Swiss cabinet members, including President Alain Berset.

“Discussions will focus on the latest developments regarding the Iran nuclear agreement,” it added. “The aim is to find ways of preserving the progress made as a result of the agreement and of ensuring the non-proliferation of nuclear weapons in the region despite the decision of the USA to withdraw from it.”

Switzerland and Iran adopted a road-map in 2016 to intensify bilateral ties when then-President Johann Schneider-Ammann visited Tehran. Talks in Switzerland will explore how relations can deepen in light of the U.S. sanctions, the government said.

The EU signatories to the 2015 nuclear pact - Germany, France and Britain - have said they want to keep the deal in place, but many companies have voiced concern over the risk of conducting business there, given the risk of U.S. sanctions.

Austria’s Oberbank said last week it would withdraw from Iran.

Reporting by Michael Shields in Zurich, Parisa Hafezi in Ankara and Francois Murphy in Vienna; Editing by Gareth Jones